If you were filling the cylinder up with water using a cone that has the same height and diameter, how many cones will it take to fill up the cylinder?

It required 3 cones to fill up the cylinder with the same height and diameter.

Step-by-step explanation:

Let the radius of the cone and cylinder be r.

Let the height of the cone and cylinder be h.

As we know that   ....(1)

It can be observed that the volume of a cone is rd the volume of the cylinder. so, multiply the volume of the cone by 3.

(From equation 1 )

Hence, It required 3 cones to fill up the cylinder with the same height and diameter.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).